Solve for dy/dx

Question

(7xy + 5)^2 = 14y

The answer is (7xy^2 + 5y) / (1 - 7x^2y - 5x)

I got that answer but the signs wrong I ended up getting (-7xy^2 - 5y) / (7x^2y + 5x - 1)

I've been doing implicit diff problems and I Get the right answer but the signs wrong and I'm not sure why that is?

If someone can show me the problem step by step on paper that would be great! Thank you!

Answer 1

(7xy + 5)² = 14y

2(7xy + 5)(7y + 7x(dy/dx)) = 14(dy/dx)

(7xy + 5)(y + x(dy/dx)) = dy/dx

7xy² + 5y + 7x²y(dy/dx) + 5x(dy/dx) = dy/dx

7xy² + 5y = (dy/dx)[1 - 7x²y - 5x]

dy/dx = (7xy² + 5y) / (1 - 7x²y - 5x)

Your answer is equivalent to mine. Just multiply the numerator and denominator of your answer by -1.

Answer 2

When I did the problem, I got the same answer you did in the same format. The answer is correct. In the answer you provided, they have taken it one step further. You might notice it isn't just one sign that isn't correct, it is all of them. So if you factor a -1 from the numerator and denominator, they can cancel and leave you with the same version that you gave. It is up to your instructor of course, but I would mark your version correct if it were me grading.